Simplify the following expression: $r = \dfrac{-24}{72q + 8}$ You can assume $q \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-24 = - (2\cdot2\cdot2\cdot3)$ The denominator can be factored: $72q + 8 = (2\cdot2\cdot2\cdot3\cdot3 \cdot q) + (2\cdot2\cdot2)$ The greatest common factor of all the terms is $8$ Factoring out $8$ gives us: $r = \dfrac{(8)(-3)}{(8)(9q + 1)}$ Dividing both the numerator and denominator by $8$ gives: $r = \dfrac{-3}{9q + 1}$